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On semi‐isogenous mixed surfaces
Author(s) -
Cancian Nicola,
Frapporti Davide
Publication year - 2018
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600436
Subject(s) - mathematics , genus , intersection (aeronautics) , surface (topology) , pure mathematics , type (biology) , construct (python library) , mapping class group , combinatorics , class (philosophy) , geometry , botany , computer science , ecology , artificial intelligence , engineering , biology , programming language , aerospace engineering
Let C be a smooth projective curve and G be a finite subgroup ofAut( C ) 2 ⋊ Z 2whose action is mixed , i.e. there are elements in G exchanging the two isotrivial fibrations of C × C . LetG 0 ◃ G be the index two subgroup G ∩ Aut( C ) 2 . If G 0 acts freely, then X : = ( C × C ) / G is smooth and we call it semi‐isogenous mixed surface . In this paper we give an algorithm to determine semi‐isogenous mixed surfaces with given geometric genus, irregularity and self‐intersection of the canonical class. As an application we classify irregular semi‐isogenous mixed surfaces withK 2 > 0 and geometric genus equal to the irregularity; the regular case is subjected to some computational restrictions. In this way we construct new examples of surfaces of general type with χ = 1 . We provide an example of a minimal surface of general type withK 2 = 7 andp g = q = 2 .